Solve 2/3u_k^2-60u_{13}+8662/3=0

$$\frac { 2 } { 3 } u _ { k } ^ { 2 } - 60 u _ { 13 } + 866 \frac { 2 } { 3 } = 0$$

Solve for u_13

$$u_{13}=\frac{u_{k}^{2}+1300}{90}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$2u_{k}^{2}-180u_{13}+866\times 3+2=0$$

Multiply 866 and 3 to get 2598.

$$2u_{k}^{2}-180u_{13}+2598+2=0$$

Add 2598 and 2 to get 2600.

$$2u_{k}^{2}-180u_{13}+2600=0$$

Subtract 2u_{k}^{2} from both sides. Anything subtracted from zero gives its negation.

$$-180u_{13}+2600=-2u_{k}^{2}$$

Subtract 2600 from both sides.

$$-180u_{13}=-2u_{k}^{2}-2600$$

Divide both sides by -180.

$$\frac{-180u_{13}}{-180}=\frac{-2u_{k}^{2}-2600}{-180}$$

Dividing by -180 undoes the multiplication by -180.

$$u_{13}=\frac{-2u_{k}^{2}-2600}{-180}$$

Divide -2u_{k}^{2}-2600 by -180.

$$u_{13}=\frac{u_{k}^{2}}{90}+\frac{130}{9}$$

Solve for u_k (complex solution)

$$u_{k}=-\sqrt{90u_{13}-1300}$$

$$u_{k}=\sqrt{90u_{13}-1300}$$

Solve for u_k

$$u_{k}=\sqrt{90u_{13}-1300}$$

$$u_{k}=-\sqrt{90u_{13}-1300}\text{, }u_{13}\geq \frac{130}{9}$$